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Chair of Applied Mathematics / Numerical Analysis
Bergische Universität Wuppertal
Faculty of Mathematics and Natural Sciences
Gaußstraße 20
D-42119 Wuppertal
Germany

Phone: +49 202 439 5296
Fax: +49 (0) 202 439 5201
E-Mail: sek-amna{at}math.uni-wuppertal.de

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Multirate

Highly integrated electric cicuits show a phenomenon called latency. That is, a processed signal causes activity only in a small subset of the whole circuit (imagine a central processing unit), whereas the other part of the system behaves almost constant over some time - is latent. Such an electric system can be described as coupled system, where the waveforms show different time scales, also refered to as multirate.

More generally, any coupled problem formulation due to coupled physical effects, may cause a multirate problem: image the simulation of car driving on the road, there you need a model for the wheel, the chassis, the dampers, the road,... (cf. co-simulation). Again each system is covered by their own time constant, which might vary over several orders of magnitude comparing different subsystems.

Classical methods cannot exploit this multirate potential, but resolve everything on the finest scale. This causes an over sampling of the latent components. In constrast, Co-simulation or especially dedicated multirate methods are designed to use the inherent step size to resolve the time-domain behaviour of each subystem with the required accuracy. This requires a time-stepping for each.

Group members working in that field

Former and ongoing Projects

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Publications

References
30.
S. Schöps; A. Bartel; H. de Gersem
Multirate Time Integration of Field/Circuit Coupled Problems by Schur Complements
Michielsen, M. and Poirier, J. R., editor, Scientific Computing in Electrical Engineering, SCEE 2010 , page 243--251.
Publisher: Springer,
2012
29.
R. Winkler
Wavelet-based Methods for Multirate PDAEs
PAMM, 10(1):435--436
2010
28.
E. J. W. ter Maten; M. Günther
Multirate time integration for multiscaled systems
Fitt, A. D. et al., editor, Progress in Industrial Mathematics at ECMI 2008
page 317--318.
Publisher: Springer, Berlin,
2010
27.
A. Verhoeven; E. J. W. ter Maten; J. J. Dohmen; B. Tasić; R. M. M. Mattheij
Terminal Current Interpolation for Multirate Time Integration of Hierarchical IC Models
Fitt, A. D. and Norbury, J. and Ockendon, H. and Wilson, E., editor, Progress in Industrial Mathematics at ECMI 2008 Volume 15 of Mathematics in Industry
page 333--339.
Publisher: Springer Berlin Heidelberg,
2010
26.
M. Striebel; A. Bartel; M. Günther
A Multirate ROW-Scheme for Index-1 Network Equations
Appl. Numer. Math., 59:800--814
2009
25.
A. Bartel; S. Knorr; R. Pulch
Wavelet-based Adaptive Methods for Multirate Partial Differential-Algebraic Equations
APNUM, 59:495--506
2009
24.
A. Verhoeven; B. Tasić; T. G. J. Beelen; E. J. W. ter Maten; R. M. M. Mattheij
BDF compound-fast multirate transient analysis with adaptive stepsize control
J. of Numerical Analysis, Industrial and Applied Mathematics (JNAIAM), 3(3-4):275-297
2008
ISSN: 1790-8140
23.
S. Knorr; R. Pulch; M. Günther
Wavelet-collocation of multirate PDAEs for the simulation of radio frequency circuits
Jäger, W. and Krebs, H.-J., editor, Mathematics - Key Technology for the Future - Joint Projects between Universities and Industry 2004-2007
page 19--28.
Publisher: Springer, Berlin,
2008
22.
R. Pulch; M. Günther; S. Knorr
Multirate Partial Differential Algebraic Equations for Simulating Radio Frequency Signals
Euro. Jnl. of Applied Mathematics, 18:709--743
2007
21.
A. Verhoeven; E. J. W. Ter Maten; R. M. M. Mattheij; B. Tasić
Stability analysis of the BDF Slowest-first multirate methods
International Journal of Computer Mathematics, 84(6):895--923
2007
20.
M. Striebel; M. Günther
Towards One-Step Multirate Methods in Chip Design
Anile, A. M. and et al., editor, Scientific Computing in Electrical Engineering. Proceedings of the SCEE-2004 Conference held in Capo d'Orlando
page 129--126.
Publisher: Springer-Verlag, Berlin,
2006
19.
S. Knorr; M. Günther
Index Analysis of Multirate Partial Differential-Algebraic Systems inRF-Circuits
Anile, A. M. and et al., editor, Scientific Computing in Electrical Engineering. Proceedings of the SCEE-2004 Conference held in Capo d'Orlando
page 93--100.
Publisher: Springer-Verlag, Berlin,
2006
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